JP2002133052A - Method for representing resource allocation problem and method for solving the problem - Google Patents

Abstract

PROBLEM TO BE SOLVED: To realize a method for representing a resource allocation problem and a method for solving the problem by using a computer with respect to a resource allocation field. SOLUTION: These methods can be applied to, for instance, the scheduling of workflow. The resource allocation problem has resource use availability and a value element which cross orthogonally with each other and is also represented by at least one domain multiset representing supply. The resource allocation problem has further a resource requirement and an optional value constraint which cross orthogonally with each other and also provides a consumer multiset representing demand. The methods define a unary constraint to the supply attribute and the demand attribute of each multiset and also define a binary constraint between consumers to each other in the consumer multiset. The resource allocation problem can be solved by applying the temporal back track algorithm to the unary constraint and the binary constraint.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

[0001] The present invention relates to the field of resource allocation. The invention relates in particular to expressing constraint problems associated with resource allocation and solving them using a computer.

[0002] The present invention is a workflow executed by a company engaged in the construction and operation of a project, a timetabling operation, a constraint-solving database, and an in-memory database. It is industrially applicable as a software product that can be used in analysis and scheduling analysis.

[0003]

2. Description of the Related Art The constraint problem relating to resource allocation is extremely difficult to solve. Consider the following simple example (we will refer to this example throughout). That is, consider a kind of logical (or physical) container, such as a factory belt conveyor. And this container has three red items,
It is assumed that two green items and one blue item are included. Further consider three consumers, named x, y, z, such as a robotic arm. Then, it is assumed that these three consumers need various numbers of items of colors assigned to them (that is, x is red, y is green, and z is blue). Here, it is assumed that x needs one item, y needs two items, and z needs three items. The problem of assessing all the possibilities of assigning the number of items to consumers is none other than the problem of permutation constrained by the number of consumers needed.
The above example is a simple problem. However, in the area of resource allocation, in at least one container, the requirements of the consumer are tied to the constraints on the item (ie, the value of the element, ie, the color in the example above), which creates a much more complex problem. For example, in a corporate workflow application, there may be more than one sales order of a particular "type" before a certain action is initiated, as well as a particular skill. It is necessary to have maintenance personnel with the following values: The value of an element can consist of a complex combination of lower values.

There are two existing approaches to exactly solving the type of assignment problem described above. Both approaches are limited by the representation of containers using mathematical sets. This allows
These two methods are constrained to treat element resources as components of the value domain.

In the first method, an extra field is added to a value set to represent the number of elements. In the simple example described above, the container elements are <red, 3>, <green, 2>, <blue, 1>. Next, the problem is the Finite-Domain BinaryConstraint Satisfaction
Problem (CSP)), usually NC-1
(Node Consistency) algorithm and FC-CBJ (Fo
rward Checking with Conflict-Directed Backjumping)
Solve by combining algorithms.

[0006] The FC-CBJ algorithm is disclosed in the following document. R. Dechter and D. Frost, "Backtracking Algorithms for Constraint Satisfaction Problems-Guidance Report," Bulletin of the University of California, Irvine, School of Information and Computer Science, Irvin, CA, April 1998 (R. Dechter and D. frost, "Bac
ktracking Algorithms for Constraint Satisfaction P
roblem-a Tutorial Survey ", tech. Rep., Universit
y of California Irvine, Department of Information
and Computer Science, Irvine, California, April 19
98) and P. Prosser, "A Hybrid Algorithm for Constraint Satisfaction Problems," Computational Intelligence, Vol. 9, No. 3, pp. 268-299, 19
93 (P. Prosser, "Hybrid Algorithms for Constrain
t Satisfaction Problem ", Computational Intelligenc
e, vol.9, no.3, pp.268-299, 1993)

[0007] Finite-Dom
ain Binary Constraint Satisfaction Problem (CS
P)) and the NC-1 (Node Consistency) algorithm are disclosed in the following literature. E. Tsusang, The Basics of Constraint Satisfaction, Academic Press, London, 1966
(E. Tsang, Fondation of Constraint Satisfacti)
on, London, Academic Press, 1966)

This technique for forcibly converting a resource attribute into a value domain has the following problems. ○ The complexity of expressing the problem increases. ○ The degree of intuition is low for system designers and problem solvers. ○ In the case of rapidly changing problems (for example, factory automation, leak flow, in-memory database, etc.),
ty) attribute does not actually change,
The value domain of an element must always be changed. For example, the availability of personnel changes much more frequently than their skills, and the number of colored items on a belt conveyor changes constantly, even though the colors of the items do not change. This type of change is inefficient in computer use. ○ As mentioned above, resource allocation is a matter of permutation.
This permutation problem can be forcibly transformed into a combination problem by treating resources as values, but the search range is much wider. It is widely recognized that existing binary CSP algorithms do not well represent the resource allocation problem.

In the second method, the resource allocation is performed separately from the main combination value constraint problem by using a sub-problem (su
b-problem) ". This is accomplished using a specialized logic programming language with very special (and usually dedicated) "constraint predicates" to solve permutation subproblems. (A guest is a concept in which a proposition describes a head, for example, the kind of "animal" in which "dogs are animals.") This technique has the following problems. ○ Formulating and solving constraint problems requires large, complex, and often specialized programming languages. ○ The resource and value constraints of the problem
Solve using components. The result is inefficient and inefficient modeling and representation of problems.

[0010]

SUMMARY OF THE INVENTION It is an object of the present invention to provide an existing CSP for solving such CSPs, regardless of whether the CSPs contain constraints on the demands of the element resources and consumers, or not. Is to improve the method.

[0011]

SUMMARY OF THE INVENTION The present invention overcomes, or at least reduces, the aforementioned limitations by expressing the resource allocation problem as a description of item supply versus consumer demand. Furthermore, unary resource constraints and 2
Define a resource allocation problem in terms of term resource constraints. The unary resource constraint and the binomial resource constraint specify both the content of the container (resource element and value element) and the demand of the consumer not by a set but by a multiple set.

The above expression makes it possible to efficiently solve resource constraints in a permutation manner in the solution of combinatorial value constraints. In addition, the expression described above exceeds the existing binary CSP, and the value constraint CSP and the resource constraint C
In addition to the combination of SPs, an extended definition that can be used to represent only existing values of a binary CSP is realized. One example of a resource constraint also provides an extended algorithm (ie, extended FC-CBJ) that can handle both value constraints and resource constraints.

Accordingly, the present invention discloses a method for expressing a resource allocation problem, and is configured as follows. (A) The resource allocation problem includes (i) at least one including both resource availability and a value for zero or more elements.
(Ii) representing by a multiset representing at least one consumer and their resource requirements, and any value constraints associated with each of said domain multisets; ,
(B) identifying, from each domain multiplex, a supply corresponding to the resource availability and orthogonal to the value for each element of the domain; (c) from each consumer multiplex, the consumer multiplex Identifying the demands that correspond to the resource requirements and are orthogonal to any constraints on the required values for each consumer.

The present invention further provides a method for expressing constraints associated with a resource allocation problem, and is configured as follows. (A) The resource allocation problem includes (i) at least one including both resource availability and a value for zero or more elements.
(Ii) representing by a multiset representing at least one consumer and their resource requirements, and any value constraints associated with each of said domain multisets; ,
(B) identifying, from each domain multiplex, a supply corresponding to the resource availability and orthogonal to the value for each element of the domain; (c) from each consumer multiplex, the consumer multiplex Identifying the demands corresponding to the resource requirements and orthogonal to any constraints on the required values for each consumer of (d), for each domain multiplex, the supply attributes of the domain multiplex and the associated consumer Defining a unary resource constraint from an association between the multiset demand attributes;
(E) defining, for each consumer multiset, binomial resource constraints between consumers in the consumer multiset in association with individual problem expressions.

The present invention further provides a method of solving a constraint problem relating to resource allocation by using a computer, and is configured as follows. (A) The resource allocation problem includes (i) at least one including both resource availability and a value for zero or more elements.
(Ii) representing by a multiset representing at least one consumer and their resource requirements, and any value constraints associated with each of said domain multisets; ,
(B) identifying, from each domain multiplex, a supply corresponding to the resource availability and orthogonal to the value for each element of the domain; (c) from each consumer multiplex, the consumer multiplex Identifying the demands corresponding to the resource requirements and orthogonal to any constraints on the required values for each consumer of (d), for each domain multiplex, the supply attributes of the domain multiplex and the associated consumer Defining a unary resource constraint from an association between the multiset demand attributes;
(E) defining, for each consumer multiset, binary resource constraints between consumers in the consumer multiset in association with individual problem expressions;
(F) applying a temporal backtracking algorithm to the unary and binary resource constraints to solve the problem.

The present invention further discloses a computer program product provided with a computer-readable medium storing a computer program for calculating a solution of a constraint problem relating to resource allocation, and is configured as follows. . The resource allocation problem includes: (i) a multiset representing each of at least one domain including both resource availability and values for zero or more elements;
i) computer code means for representing by at least one consumer and their resource requirements, and a multiset representing any value constraints associated with each of said domain multisets, and from each domain multiset:
For each element of the domain, the computer code means for specifying the supply corresponding to the resource availability and orthogonal to the value, and from each consumer multiplex set, the resource requirements for each consumer of the consumer multiplex set And computer code means for identifying a demand orthogonal to any constraints on the required values, and for each domain multiplex, an association between the supply attribute of the domain multiplex and the demand attribute of the associated consumer multiplex. And computer code means for defining unary resource constraints and, for each consumer multiset, binomial resource constraints between consumers in the consumer multiset in association with individual problem expressions. , Temporal back to the unary and binary resource constraints By applying a rack algorithm,
Computer code means for solving the problem.

The present invention further discloses a computer system programmed to calculate a solution to a constraint problem relating to resource allocation, and is configured as follows. A memory for storing a computer program, and data input means for inputting the resource allocation problem as at least one domain of an element, each of the elements having a resource availability, at least one of A multi-set representing each of at least one domain comprising: (i) data availability means for each of two consumers having resource requirements; and the resource allocation problem comprising: (i) both resource availability and values for zero or more elements. And (ii) at least one consumer and their resource requirements;
And expressed by a multiplex set representing an arbitrary value constraint associated with each of the domain multiplex sets. From each domain multiplex set, for each element of the domain, a value corresponding to the resource availability and a value Identify orthogonal supplies,
From each consumer multiplex set, for each consumer of the consumer multiplex set, specify a demand that corresponds to the resource requirement and is orthogonal to any constraint on the required value, and supplies the domain multiplex set for each domain multiplex set. Unary resource constraints are defined from the association between the attributes and the demand attributes of the associated consumer multisets, and for each consumer multiset, the binomial resource constraints between the consumers in the consumer multiset are defined for each individual problem. Executing the computer program in response to the resource allocation problem so as to define the expression in relation to an expression and apply a temporal backtracking algorithm to the unary and binary resource constraints to solve the problem. A processor.

[0018]

DETAILED DESCRIPTION OF THE INVENTION It is useful to first consider the existing CSP (Constraint Satisfaction Problem), especially the terminology of the Binary CSP, and then provide a detailed definition of the resource constraints that contribute to the present invention. is there.

Value Constraint Satis
faction Problem)

Binary value constraint satisfaction problem (V, D, U, B)
Is a set V of n variables {v ₁ , ..., v _n }, a set D of _n individual value domains {D ₁ , ..., D _n }, n individual unary Value constraints (or individual unary value relations)
_{{U 1, ..., U n} } consisting of the set U (except U _i ⊆D _i for each domain), and, second term value constraint (or two-term value relationship) between v _i and v _j It consists of a set B consisting of B _ij . The "pre-processing" application of the unary value constraint is that for each domain (in order to achieve node consistency) B _ij is a subset of the product of the unary relations,
That is, it is assumed that B _ij ⊆U _i × U _j is satisfied.

The ordered pair (v _i , a _i ) represents the instantiation of the variable v _i at the value a _i from the domain. (Illustration is an example of assigning a value to a variable.
ce).) If a _i satisfies any unary value constraint relates v _i, ordered pair (v _i, a _i) is said to be "consistent (consistent)." An example of a subset of variables is an ordered pair ((v ₁ , a
_1), ..., it is denoted by _{(v i, a i))} . This set (ie, a partial example) is usually (a ₁ , ...,
_ai ). A set is consistent if all ordered pairs in the set are consistent and all binomial constraints on the variables in the set are satisfied. The matching partial instances are called partial solutions. A consistent set containing all variables is the solution. It is assumed that a fixed order exists in the example of the variables.

Multi-sets

The multiset m is a function m∈ [D → N] for a non-empty domain set D (where N is a non-negative integer, and [D → N] is all functions from D to N). Is a set of The integer function m (e) ∈N is the element e∈
It is the number of instances of D. m (e) ≠ 0
, The element e is said to belong to m. If m (e) is 1 for all elements e∈D, the multiset m is
It is equal to the set D in which it is defined. Multiple sets, _{usually, m (e 1) 'e} 1 + ··· + m (e n)' abbreviated as e _n. For example, the multiset of FIG. 1 is 3 ′ red + 3 ′ green + 1
'Write blue. Here are some useful relationships defined for multisets. m ₁ ≧ m ₂ = [∀e∈D: m ₁ ≧ m ₂ ] (comparison) m ₂ −m ₁ = [Σ _eD (m ₂ (e) −m ₁ (e)) ′ e] (difference)

Unary Resource Constraint
ts)

Unary and binary resource constraints form the mathematical basis of the present invention. First, unary resource constraints are defined.

For a multiset m over each element e∈D and D, we will hereinafter refer to m (e) as the supply of e in m. The binary CSP is extended to include the unary resource constraint to be (V, D, M, U, B). Here, M, the values e _i ∈D value domain is like having a feed m _i (e), individual values domain _{{D 1, ..., D n} } n -number of multiset over { m _1, ..., a set consisting of m _n}.
Further, each variable has an associated demand (denoted as δ _i ). δ _i is the number of instances required for any value in the value domain of the variable. The ordered pair of variable-demand is
(V _i, δ _i) is represented as, using [delta] _i 'v _i becomes notation to indicate that itself is a multi-set. From the above, V is a set of n variable-demand pairs, as shown in equation (1). V = {δ ₁ 'v ₁ , ..., δ _n ' v _n } (1)

The ordered set (δ _i , v _i , a _i ) has the value a _i ∈D _i
Represents an example of a variable v _i having an instance δ _i of m (a _i )
≧ [delta] _i, i.e. a case _i supply of satisfying the demands of at least v _i, the ordered pair _{(δ i, v i, a} i) is the resource matching (r
esource consistent) is said to be. An example in the multiple set is abbreviated as δ _i ′ a _i j. The demand for each variable is
Represents an implicit unary value constraint on the domain. This is called a unary resource constraints for the variable v _i, is defined by the following equation (2). _{μ i = D i - {e∈D} i | m i (e) <δ i} (2)

A consistent example cannot be obtained from a value that results in a supply that does not meet the demand for the variable. This unary resource constraint is orthogonal to any unary value constraint that can additionally be applied to the variable. When supply and demand are all ones, the resource constraint vanishes (or transforms into an implicit constraint that must have a value in the domain to be considered). As with the unary value constraint,
Unary resource constraints can also be realized by preprocessing the domain.

Binary Resource Constraint
nts)

Here, the previous definition is further extended to 2
Include term resource constraints. As a major aspect of the binomial resource constraint, we introduce the "sharing" of one domain between multiple variables. Let V be an n-empty set of variables-demand {V ₁ , ..., V _n }. Each is assigned to an individual value domain. Therefore, the following equation (3) is obtained. V = ｛｛δ _1i 'v _1i , ..., δ _1j ' v _1j ｝, ..., ｛δ _ni 'v _ni , ..., δ _nk v _nk ｝｝ ・ ・ ・ (3) V ₁ ∩V ₂ ∩ ... ∩V _n = φ, that is, one variable is associated with only one domain. As in the case of the domain, each set of the variable-demand pair is a multiplex set, so that V can be expressed as a set of multiplex sets of variables as shown in Expression (4). V = {δ _1i 'v _1i + · + δ _1j ' v _1j , ..., δ _ni 'v _ni + · + δ _nk v _nk ｝ ・ ・ ・ (4)

An example A _i of a variable multiset V _i consisting of k variables is δ _i1 ′ a _i1 + · + δ _ik ′ a _ik where a _ik ∈D _i
Becomes If m _i ≧ A _i , the example A _i is resource consistent. Multiple variables in a multiple set can be illustrated with the same value.
Thus, the exemplary total demand for the value e∈D _i is A
_i (e).

Resource consistency can be expressed as a set of binomial constraints on a variable multiset. Variable - partially illustrated are resources matching the set V _i demand versus [delta] _i1 'v _i1
In the case of + · + δ _ij ′ v _ij , the efficient multiset maintained for the example of variable v _{ij + 1} is m _{ij + 1} = m _i −A _ij
It is. Then, if m _{i + 1} ≧ A _{ij + 1} , a partial example A
_{ij + 1} is resource consistent. In other words, each variable of V _i is,
Constrained by all preceding instances of variables sharing the same value domain (this is complementary to any implicit unary resource constraint). This means that intuitively, the preceding example "starved (st
arve) ”. Variable - a set of demand-to-V _i of the variable v
A resource binomial constraint on _ij is defined as in equation (5). β _ij = D _i- {e∈D _i | m _i <(A _ij-1 (e) + δ _ij )} (5)

Expression of resource allocation problem

FIG. 1 is a diagram illustrating the simple problem described above expressed as a unary and binary resource constraint problem. The domain multiset 10 includes three red items, two green items, and one blue item. This means
The number of items is "resource availab
ility), while the color indicates "value". All three variables x, y, z in the associated consumer multiplex 20 are competing for resources from the domain multiplex 10. In more complex resource allocation problems, there are at least two domain multisets, each of which is associated with a consumer multiset.

The supply of each item in the domain is specified from the domain multiplex set 10. That is, the red item is 3
Pieces, two green items, and one blue item.
The supply of each item in the domain multiplex 10 is orthogonal to its value (color in this example). Thus, for example, adding a fourth red item to the domain 10 does not affect the value representation. In other words, unlike existing expressions of such problems, usability and values are treated as unrelated.

The demand for each variable is expressed by the consumer multiset 2.
Specify from 0. That is, one variable x and two variables y
And three variables z. The demand for each variable is orthogonal to any constraints on the values that can be assigned to each variable.
Therefore, the following items hold. (I) Changes that follow the demand for any variable as a result of redefining the problem, of course, do not affect the values that can be assigned to that variable. (Ii) Subsequent redefinition of the problem to include unary and / or binomial constraints on the variables does not require a change in demand for the individual variables. ("A and / or B" stands for "A and B, A, or B").

Since the variables y and z have non-unary demands, they impose unary resource constraints on the domain multiset 10.
Therefore, the following unary resource constraint is defined. (I) Unary resource constraint from the variable y to the domain 10.
As a result, all items whose supply is less than 2 (which is the demand for y) need not be considered. (Ii) Unary resource constraint from the variable z on the domain 10.
As a result, all items whose supply is less than 3 (which is the demand for z) need not be considered.

If a variable in the consumer multiplex 20 is exemplified by the value of an item, the supply of the item is reduced by an amount equal to the demand of the variable. Based on the optional but fixed ordering of the variables, a set of binary resource constraints is defined between the variables in the consumer multiset 20. These binary resource constraints are defined as binary resource constraint diagrams. The structure of the binomial resource constraint diagram depends on how the order of example variables is selected. If the binomial resource constraint exemplifies all variables in the same consumer multi-set 20, the supply of items for subsequent variables is "loss (de
privation) ". FIG. 2 is a binomial resource constraint diagram for the problem of FIG.
The case of performing in the order of y and z is shown.

In general, a k-term (k ≧ 1) value constraint can exist for (or between) any variables involved in a resource constraint. The algorithm shown below facilitates this. However, the resource constraint diagram and the value constraint diagram (both used in the algorithm shown below) are orthogonal to each other as described above (see FIG. 1). If the set of variable-demand pairs is a single set, then only unary resource constraints can exist. If all demands are 1, the value constraint diagram disappears. With the above definition, a generalized value-resource CSP can be realized. The existing value-only problem and the resource-only problem shown in FIG. 1 are each a form of generalized value-resource CSP.

The advantage of treating value constraints and resource constraints as orthogonal to each other (ie, separate) within one problem is that
It is as follows. ○ The problem can be solved efficiently by a single algorithm. ○ The problem expression can be intuitive. ○ Even if resources change, it is not necessary to change the value attribute of the element. ○ The algorithm shown below does not require a special programming language and does not need to support a special environment. The algorithm shown below can be easily integrated into existing designs and systems. In addition, the algorithm shown below is for "lightweight"
t) "can be incorporated into the software.

Generalized problem expression

FIG. 1 shows an example of a single domain multiset containing six elements. The six elements represent the usability and the value. A single consumer multiplex is associated with the value. This single consumer multiplex has three consumers and their resource constraints. In this example, there are no value constraints.

FIG. 3 is a diagram showing a generalized expression of the resource constraint problem. In FIG. 3, there are N domains 30 _N ,
Each domain is represented by a multiple set of elements 32 and 34. Each element has a resource availability ("ra") and a value ("v"). Each domain multiplex has a different element number (eg, 32 _i , 34 _j, etc.). The “resource availability (ra)” is expressed so as to be orthogonal to the “value (v)” and expresses supply.

There is a consumer multiset 40 having a number of consumers 42 _k . Each consumer has a resource requirement ("rr") and an optional value constraint ("vc"). “Resource requirement (rr)” is expressed so as to be orthogonal to “value constraint (vc)”. Consumer multiset 4
The arc connecting between 0 and domain multiset 30 includes various arc consumers (e.g., among the k consumer, k-1 is a demand regarding multiset 30 ₁ cage, k-4 has a demand regarding multiset 30 _N, etc.). Thus, "l" is a subset of "k" consumers.

Resource Constraint FC-CBJ (Forward Checki
ng with Conflict-Directed Backjumping)

In one embodiment, the present invention relates to an FC (Fo)
rward Checking: Forward Checking?
Provides an extension of the FC-CBJ algorithm derived from
You. FC operates at the value CSP as follows.
First, a partial example (a₁, ..., a _i) And the variable v_i And not illustrated
Variable v_j , V_k , V_l ｛B between_ij, B_ik, B
_ilConsider the set of｝. And example a_i Constraints and
For all "removed" inconsistent values
And examine the domain of these variables. As a result of the investigation,
Without the domain, the partial examples would be consistent and
Number v_{i + 1} Try to extend. If you have an empty domain,
Restore the empty domain and return the variable v_i Another value for
Try. If this is not possible, backtrack
Perform

FC is applied to resource constraints as shown below.
can do. That is, the domain D_ikTo share
Set V of number-demand pairs_i From equation (5) above,
Number v _ikAre all variables v exemplified before the variable
_i1, ..., v_ik-1It can be seen that it is restricted by
Partial example A_ij-1Value e∈D remaining after_i The supply of
m_i(e) -A_ij-1 (e). This supply is the demand δ_ij,
δ_ikSatisfies both, but the following v_ijTo
The assignment is a variable v_ikHungry for the supply of
("Starve").
Therefore, the variable is_ijTo
Variable e which is not assigned until reassignment
You are in a collision. FC is (i) remaining for each variable
Maintain a running tally of supply that is
Forward supply-demand ch for all unexemplified variables
Check (only needed for the last assigned value)
This can be realized by executing. (Driving intuition
Is a dynamic record of entry and exit.)

[0048] CBJ (Conflict-Directed Backju
Adding a mping) improves the efficiency of backtracking by using a conflict set. Since consistency is determined by FC, CBJ can handle both value constraints and resource constraints equally well. Each time a value is removed from the domain D _j by a forward consistency check on the example (a ₁ ,..., A _i ), a variable v _i is added to the unique collision set of v _j . When all values have been removed from D _j, the collision set of v _j (except v _i ) is
v Because _i would be integrated with the set of the collision, try another example. If this is not possible, the algorithm, v directly from the v ₁ ... v _i-1 present in the collision set in _i to the last to the illustrated variable to "back jump (backjump)". As a result, the new collision set of v _i is integrated with the collision set of the target variable (ie, the last exemplified variable), and all existing collisions remain. CBJ to solve resource constraints
Is not necessary. However, since CBJ is efficient, variables sharing a domain can be discrete (in the order of illustration) with unrelated variables. This embodiment (for multiple sets)
Name it FC-CBJ-M. The operation will be described below.

FIG. 4 is a diagram showing a step-by-step solution of the problem of FIG. 1 using FC-CBJ-M. FC-CBJ
The -M algorithm requires only one additional storage component in addition to the standard FC-CBJ algorithm. This additional storage component represents an efficient multi-set of each domain element (ie, each domain value) (ie, the remaining supply). This additional storage component is in the form of an array for each domain, the storage complexity of which is Q _nm . Here, n is the number of value domains, and m is the maximum number of values in any domain. From FC-CBJ, conflict of each variable
In the (collision) array, the domain values in a collision state with the preceding example are recorded. Each entry, if present, points to the conflicting variable numbers 1, 2, 3 (x, y, z, respectively). A value of 0 indicates a unary collision (and is therefore an unusable value).

FIG. 4 shows the result of the permutation search leading to the solution of the present example.
FIG. 7 is a diagram showing how both the value of the supply array and the value of the conflict array change.

Step 1 shows the initial supply conditions for each value and how the demand for each variable (which is kept constant) imposes a unary resource constraint. As mentioned above, if these constraints fail, it will conflict
Reflected in the array. In this example, the value y cannot be assigned to the variable y, but only the value red can be assigned to the variable z.

In step 2, the first variable x is temporarily assigned to the value red. Since the variable x has a demand of 1, this demand is subtracted from the entry in the supply array corresponding to the value red. Since the variable x has a binomial resource constraint with the remaining variables, each constraint is tested by checking for at least one value that has sufficient supply capacity.
Such a test is not performed on the variable z, since there is no longer a value with a supply of 3. As a result, the conflict array for the variable z is updated to show all values that suddenly become unavailable. By assigning variable x, variable z is "starve" for all values.
Will be. Therefore, this assignment is not feasible and is discarded (thus, the value of the supply array and the conflict
Undo the array value).

In step 3, the variable x is assigned to the next available value green. As a result, the value green supply is reduced by one. This causes a conflict with the variable y, but does not starve any variables. Therefore, this assignment is maintained.

In step 4, the next variable y is assigned to the first (and only) free value red. As a result,
The supply of value red is reduced by two. This will discard this assignment because the variable z will "starve" for multiple values. Since there is no longer any free value in the conflict array for the variable y, a "backjump" is made to the assignment of the highest conflicting variable (ie x) (as FC-CBJ shows). It is safe to do. Again, the values of the supply array and the conflict array are updated at each back jump step.

In step 5, the variable x is assigned to the next available value blue. As a result, the supply of value blue is reduced by one (and value blue becomes unavailable). As a result, since the variable y and z cannot use this value blue because of the unary value constraint, no collision occurs with respect to the variables y and z.

In step 6, the next variable y is assigned to a first free value red. As a result, the value red supply is reduced by two. Then, repeating step 4, this assignment is discarded because the variable z is "starved".

In step 7, the variable y is assigned to the value green. As a result, no collision occurs with respect to the variable z,
Maintain quotas.

In step 8, the variable z is simply assigned to the first and only free value red. This completes the solution of the problem. Since the problems cited here are simple in nature, the efficiency gained by using CBJ is impaired. But realistic (and complex)
In practice, this is not usually the case (ie, the benefits of using CBJ can be enjoyed).

FC-CBJ-M algorithm

The FC-CBJ-M algorithm is provided as four components. One of them is F
It is unique to C-CBJ-M. But the remaining three
One is an extension of the original FC-CBJ. The following global constants are determined by the definition of the CSP. That is, modecount is the number of variables. For each variable n, demand _n is demand, B _n is a set of higher numbered variables constrained by _n , and V _n is the definition of n It is a set of variables that share a region but have ≠ n. V
_n is unique to FC-CBJ-M. Each variable n
Requires the following global storage. That is, D _n is a value domain, M _n is a multiplex set for the supply of D _n or n, and mask is a large value indicating a domain value that is in conflict with the preceding variable. Is an array of | D _n |, where conflict indicates which preceding variable is in collision with n, and has a size of (n
-1) is a Boolean array. _Mn is FC-CB
It is unique to JM.

Each variable n is an assignment function Assign _n , a unary value constraint function Unary _n (value
_n ) and a (possibly null) binary value constraint Binary _n (value _n , value _m ) on the forward variable. There is also a global function RecordSolution () to get the assignment of variables when the solution is reached.

Algorithm 1: FC-CBJ-M ()

Comment: value—find solution of resource CSP local valid for n ← 1 to nodecount do begin valid ← 0 for i ← 1 to n do begin conflict [n] [i] ← false end for i ← 1 to | D _n | do begin if Unary _n (i) = true and M _n [i] ≧ demand _n then mask [n] [i] ← OK valid ← valid + 1 else mask [n] [i] ← 0 end end if valid = 0 then return () end end DoNode (1)

Algorithm 2: DoNode (n)

Comment: Recursively process node n and all nodes deeper than it. Local bjnode for i ← 1 to | D _n | do begin if mask [n] [i] = OK then if ResourceFC (n, i ) = true then if ValueFC (n, i) = true then ok ← true Assign _n (i) if n = nodecount then RecordSolution () return (0) else M _n [i] ← M _n [i]-demand _n bjnode ← DoNode (n + 1) M _n [i] ← M _n [i] + demand _n if bjnode ≠ n then return (bjnode) end end end end end end bjnode ← n-1 while bjnode> 0 and conflict [n] [Bjnode] ≠ true do begin bjnode ← bjnode-1 end if bjnode> 0 then for j ← bjnode-1 downto 1 do begin if conflict [n] [j] = true then conflict [bjnode] [j] ← true end end end return (bjnode)

Algorithm 3: ResourceFC
(N, i)

Comment: Process binary resource constraints on nodes n and value [i] locasl supply, valid supply ← M _n -demand _n for each m m V _n | m> n do begin conflict [m] [n] ← false valid ← 0 for j ← 1 to │D _n │ do begin if mask [m] [j] ≥ n or mask [m] [j] = OK then if J = 1 and demand _m > supply then mask [m ] [J] ← n conflict [m] [n] ← true else mask [m] [j] ← OK valid ← valid + 1 end end end if valid = 0 then for j ← n-1 downto 1 do begin if conflict [M] [j] = true then conflict [n] [j] ← true end end return (false) end end return (true)

Algorithm 4: ValueFC (n;
i)

Comment: Process binomial constraint on node n and value [i] local wipelevel, valid for each m ∈ B _n do begin if V _m ≠ φ then wipelevel ← n + 1 else wipelevel ← n conflict [m ] [N] ← false end valid ← 0 for j ← 1 to │D _m │ do begin if mask [m] [j] ≥ wipelevel or mask [m] [j] = OK then if Binary _n [m] (i , j) ≠ true then mask [m] [j] ← n conflict [m] [n] ← true else mask [m] [j] ← OK valid ← valid + 1 end end end if valid = 0 then for j ← n-1 downto 1 do begin if conflict [m] [j] = true then conflict [n] [j] ← true end end return (false) end end return (true)

First, the main procedure FC-CBJ-M
(Algorithm 1) initializes global storage, performs unary value constraint checking, and calls DoNode to manage the search. The extension of FC-CBJ is
Check for unary resource constraints (M _n [] ≧ demand _n ). Recursive function DoNode (algorithm 2)
Manages FC consistency checks, performs back jumps, and records all solutions. FC-CB
Another extension of J is Res (for resource constraint checking).
calling sourceFC and adjusting the supply _Mn before and after a recursive call to itself. The function ResourceFC (algorithm 3) is FC-C
Assigned to variable n, D _n , unique to BJ-M
All binomial resource constraints for [i] are checked forward. ResourceFC is tentatively reducing the supply for the assigned value, thereby checking if any of the forward variables result in starvation. All such inconsistencies are recorded in the mask and conflict arrays. Finally, ValueFC
(Algorithm 4) assigns D _n [i] to variable n
Are forward checked. The condition description “if V _m ≠ φ” and its associated actions are extensions needed to prevent a previous call to ResourceFC from erasing any collisions or masks generated.

Further Resource Allocation Problem

A second example that illustrates the use of resource constraints is that both unary and binary resource constraints, and both unary and binary constraints work together to solve a simple scheduling problem. This is to explain the usual way. This example shows a non-elementary domain entry (ie, tuple)
It also shows how to use, and how to use a multi-valued domain.

Description of the problem

The problem exemplified here is for scheduling two different types of resources. These two different types of resources each have limited availability and have specific resource demands and value constraints over a fixed range of time slots. The problem is 9 am
There are two different types of staff (lecture (le
and pools of tutors). The supply of both types of staff varies from hour to hour. Timetables have created a demand for resources of both types of staff for various classes. As new constraints arise on the type of staff required for a given lesson, it becomes necessary to schedule another lesson. The desired solution is
Assigning a start time and a staff type for each class. FIG. 5 is a diagram showing the supply of lecturers and tutors from 9:00 am to 1:00 pm.

Using a value set of the form <stuff type, time> (where "L" represents a lecturer and "T" represents a tutor), the total stuff supply is represented by a single multiset value It can be expressed by a domain. 1 '<L, 9>+3'<T,9> +1 '<L, 10>+3'<T,11> +2 '
<L, 12> +1 '<T, 12>

This equation indicates that, for example, at 9 am, one lecturer and three tutors are available.

To account for constraint satisfaction across multiple value domains, a "qualifier" domain is introduced.
This only includes the stuff-type single set shown below. 1 '<L> or 1'<T>

The consumer multiset consists of four components, corresponding to individual lectures that assign staff to demand and value constraints. First state: Lecture 1 takes place at any time and requires two lecturers. Second state: Lecture 2 requires two staff members of one type per hour and one staff member of the opposite type per hour for any two consecutive hours. Third state: Lecture 3 takes place at any time and requires three tutors. Fourth State: Lecture 4 requires one staff member of the type specified in the "qualified" domain for any two consecutive hours.

FIG. 6 shows a generalized resource of the above-mentioned problem.
It is a figure expressed as a value constraint satisfaction problem. Lectures 2 to 4 in which each is expressed as a multiset demand with value constraints
Is as shown below.

Lecture 1: 2 ′ <L, t ₁ > where t ₁ is a variable corresponding to the start time of lecture 1.

There is one unary resource constraint (requires two staff members) and one unary value constraint (the staff members must be lecturers).

Lecture 2: 1 ′ <s ₁ , t _2a > +2 ′ <s ₂ , t _2b > [s ₁ ≠ s ₂ AND abs (t _2a −
t _2b ) = 1] where s ₁ and s ₂ are variables corresponding to different staff types assigned to each time, and t _2a and t _2b are the start times of two lessons with lecture 2 as a component. Is the corresponding variable.

[0083] One of the unary resource constraints (staff of the type s ₂ 2 people required) and two two-term value constraints (two staff type must be different, the start time of the two classes has not been adjacent Must exist).

Lecture 3: 3 ′ <T, t ₃ > where t ₃ is a variable corresponding to the start time of lecture 3.

There is one unary resource constraint (requires three staff members) and one unary value constraint (the staff members must be tutors).

Lecture 4: 1 ′ <x, t _4a > +1 ′ <x, t _4b > [t _4b = t> _4a +1] where x is a variable corresponding to the stuff type, and t _4a
t _4b is a variable corresponding to the start time of two classes in which lecture 4 is a constituent element.

There are two binary value constraints (the stuff type must be the same in both classes and the start times of the classes must be adjacent). In addition, there is one binomial constraint with a "qualified" variable x (the stuff type must be met).

Solution of the problem

This problem can be solved by first applying unary resource constraints and unary value constraints to reduce the efficient value domain in which each demand “sees”. Demand with efficient domain arcs decreases as follows. 2 '<L, t> ₁ (2'<l,12>) 2 '<s ₂ , t> _2b (3'<T,9> +3 '<T, 11>+2'<L,12> ) 3 '<T, t ₃ >(3'<T,9> +3 '<T, 11>)

The next step in solving the problem is to select an arbitrary but fixed order of demand satisfaction (and thus assign variables). This includes non-elementary multisets (1 '<
s ₁ , t _2a > +2 ′ <s ₂ , t _2b >, 1 ′ <x, t _4a > +1 ′ <x, t _4b >) is separated into elementary multiplex sets. It illustrates a "qualified person" variable x, variable and variable set _{t 1, <s 1, t} 2a>, <s 2, t 2b>, t 3, <x, t
_4b > The demand for each can be satisfied.

FIG. 7 is a binomial constraint diagram for this problem expressed as an elementary multiplex set. The resource constraint indicated by the broken line is made redundant by the value constraint process.

The final step in solving this problem is to set the depth to the first
Is to perform a search that has been made. The algorithm iteratively assigns allowed values to demand variables, forward-checks all resource and value constraints, and advances to the next variable (or set) even if there are solutions that cannot be eliminated by this check. . Always backtrack or jump back immediately when erasing the solution.

FIG. 8 is a solution diagram for a predetermined variable and set (assignment is performed from top to bottom, from left to right). The variables X, t have only one assignment. The pair <s ₁ , t _2a > is, for all possible assignments of <s ₂ , t _2b > for all assignments, except for <L, 10>,
All of the value constraints have failed. Similarly, then the value 1
Assigning 1 to t ₃ gives a sufficient set of resources <x, t _4a >, <x, t
_4b > is eliminated (through resource constraints) to satisfy both value constraints.

As a result, there is only one solution shown below. _{x = T t 1 = 12 <} s 1, t 2a> = <L, 10><s 2, t 2b> = <T, 11> t 3 = 9 <x, t 4a> = <T, 11>< x, t _4b > = <T, 12>

If 1 ′ <L> is included in the “qualified person” domain, no solution exists.

Referring to FIG. 6, the following can be understood. That is, the above-described solution process is to “shuffle” the block called demand in a permutation and combination, and “fit” inside the supply so as to satisfy the value constraint (eg, order). is there. By orthogonally separating supply / demand from values, permutational and combinatorial searches are possible. This is a very efficient method, as opposed to a purely combinatorial search that is possible with only value constraints.

Implementation on Computer Platform

The FC-CBJ algorithm can be implemented using a computer program product together with the computer system 100, as shown in FIG. The FC-CBJ algorithm may be implemented, among other things, as software running on computer system 100, i.e., computer readable program code.

The computer system 100 includes a computer 150, an image display device 110, and an input device 1.
30, 132 are provided. In addition, computer system 100 can include a number of other output devices, including reproducers connected to computer 150, such as line printers, laser printers, plotters, and the like. The computer system 100 has a communication input / output (I
/ O) Via an interface 164, it can be connected to at least one other computer using a suitable communication channel 140, such as a modem communication path or an electronic network. The electronic network includes a LAN (loca
l area network), a wide area network (WAN), an intranet, and / or the Internet 120.

The computer 150 includes the control module 1
66, RAM (random access memory) and ROM (read
-only memory), input / output (I / O) interfaces 164, 172, image interface 160, and generally storage 162.
At least one storage device.
The control module 166 is a CPU that executes (ie, runs) computer readable program code that performs a particular function (or set of related functions).
(Central processing unit).

The image interface 160 is connected to the image display device 110, supplies an image signal from the computer 150, and uses the image signal for display on the image display device 110. The user input for operating the computer 150 is
The input devices 130, 1 via the I / O interface 172
32.
For example, a user of computer 150 may have a keyboard and / or I / O interface 130 as I / O interface 130.
As the / O interface 132, a pointing device such as a mouse can be used. The keyboard and the mouse realize input to the computer 150. The storage device 162 can be composed of at least one of the following. That is, floppy (R)
Numerous non-volatile storage devices known to those skilled in the art, such as disks, hard disk drives, magneto-optical disks, CD-ROMs, magnetic tapes, and the like. Each component in the computer 150 is typically connected to other components via a bus 180 comprising a data bus, an address bus, and a control bus.

The algorithm described above is applied to a computer
This is accomplished by instructions in software that system 100 executes. Again, the algorithm described above is
It can be implemented as at least one module that implements the steps of the method.

In particular, the software described above can be stored on a computer readable medium such as storage device 162. Alternatively, the software described above
It can also be downloaded from a remote location such as a location (ie, site) on a network such as the Internet via the I / O interface 164 and the communication channel 140. The computer system 100 includes a computer-readable medium recorded so as to execute the above-described software instructions (that is, program codes). The use of computer system 100 advantageously provides an apparatus for constructing routine symbols for computer programs according to embodiments of the present invention.

The computer system 100 has been presented for the purpose of explanation, and other configurations may be employed within the scope and spirit of the invention. What has been described above is merely one example of a type of computer (or computer system) that can be used to implement embodiments of the present invention. Typically, the processes of the embodiments of the present invention exist as software (ie, a computer readable program recorded on a hard disk as a computer readable medium).
(As a code) and read and controlled using control module 166. Intermediate storage of the program code and all data including entities (entities), tickets (tickets), etc. can be realized by using the memory 170 in cooperation with the storage device 162 if possible.

In one example, the above program is a CD
-Encoded on a ROM or floppy disk (both shown generally as storage device 162) and can be provided to the user. Alternatively, the user
The above program can be downloaded from a network via a modem device connected to the computer 150. Further, the computer system 100
Can load the software described above from another computer-readable medium. This includes magnetic tape, ROM or integrated circuits, magneto-optical disks, wireless or infrared communication channels connecting computers to other devices, computer readable cards such as PCMCIA cards, e-mail and recorded on Internet sites. The information may include the Internet 120 and an intranet that include the obtained information. These are merely examples of equivalent computer-readable media.
Other computer readable media may be used within the scope and spirit of the invention.

The above-described algorithm can be implemented in a centralized fashion on one computer system 100, or the various components are distributed among several interconnected computer systems. It can also be realized in a distributed form.

A computer program means or computer program in the context herein allows a system with information processing functions to convert a particular function directly or (a) into another language, code or notation. ,
(B) A set of instructions intended to be executed after being reproduced on another medium or after performing only one of them, expressed in any language, code, or notation.

Although only a few embodiments have been described, it will be apparent to those skilled in the art in light of this disclosure that many variations and / or modifications may be made within the scope and spirit of the invention.

The following items are disclosed as a summary. (1) A method of expressing a resource allocation problem,
(A) The resource allocation problem includes (i) at least one including both resource availability and a value for zero or more elements.
(Ii) representing by a multiset representing at least one consumer and their resource requirements, and any value constraints associated with each of said domain multisets; ,
(B) identifying, from each domain multiplex, a supply corresponding to the resource availability and orthogonal to the value for each element of the domain; (c) from each consumer multiplex, the consumer multiplex Identifying a demand that is orthogonal to any constraints on the required values that correspond to the resource requirements for each of the consumers. (2) The method according to (1), wherein each domain multiplex set is represented as a set of pairs of resource availability and value elements. (3) The method of (2) above, wherein each of the pairs comprises an arbitrarily complex set of values and resource availability. (4) The method according to (1), wherein the consumer multiplex is represented as a set of resource requirements and value constraints. (5) The method according to (4), wherein the value constraint comprises a variable or a value, or a combination of both. (6) For each domain multiplex, the supply is represented in terms of the sum of its base set and the number of occurrences of each element of the base set, and for the consumer multiplex, the demand is The method according to (1), wherein the method is expressed in terms of a sum with the number of occurrences of each element of the basic set. (7) A method for expressing constraints associated with a resource allocation problem, comprising: (a) defining the resource allocation problem
(I) a multiplex set representing each of at least one domain including both resource availability and values for zero or more elements; and (ii) at least one consumer and their resource requirements, and the domain multiplex. (B) from each domain multiplex set, a value corresponding to the resource availability and from each domain multiplex set, Identifying orthogonal supplies; (c)
From each consumer multiplex set, for each consumer in the consumer multiplex set, identifying a demand corresponding to resource requirements and orthogonal to any constraint on required values; and (d) for each domain multiplex set, Defining a unary resource constraint from the association between the supply attributes of the multiset and the demand attributes of the associated consumer multiset; and (e) for each consumer multiset, between the consumers in the consumer multiset. Defining binomial resource constraints in association with individual problem expressions. (8) A unary resource constraint is defined for each consumer, and the supply of each consumer determines the consumer's view of the domain only by the elements of the domain having a supply larger than the demand of the consumer. The method according to (7) above, wherein (9) The method of (7) above, wherein for any given order of assignment of values to consumers, there is a binary resource constraint between one consumer and all subsequently assigned consumers. (10) By assigning a value to a certain consumer, a binomial resource constraint dependent on the satisfied unary resource constraint of the consumer is realized, and as a result, the assigned value is increased by the magnitude of the demand of the consumer. The method of (9) above, wherein the supply of N.I. is reduced and availability restrictions constrain the assignment of this same value to the next consumer. (11) The method according to (7), wherein each domain multiplex set is represented as a set of pairs of resource availability and value elements. (12) The method of (11) above, wherein each of the pairs comprises an arbitrarily complex set of values and resource availability. (13) The method according to (7), wherein the consumer multiplex set is represented as a set of resource requirements and value constraints. (14) The method according to the above (13), wherein the value constraint comprises a variable or a value, or a combination of both. (15) For each domain multiplex, the supply is represented in terms of the sum of its base set and the number of occurrences of each element of the base set, and for the consumer multiplex, the demand is The method according to (7), wherein the method is expressed in terms of the sum of the number of occurrences of each element of the basic set. (16) A method for solving a constraint problem relating to resource allocation using a computer, wherein (a) the resource allocation problem includes at least (i) both a resource availability and a value for zero or more elements. Representing by a multiset representing each one of the domains, and (ii) a multiset representing at least one consumer and their resource requirements, and any value constraints associated with each of the domain multisets. (B) identifying, from each domain multiplex, a supply corresponding to resource availability and orthogonal to a value for each element of the domain; (c) from each consumer multiplex, the consumer For each consumer in the multiset, a step that identifies the demand that corresponds to the resource requirements and is orthogonal to any constraints on the required values. (D) defining, for each domain multiplex, a unary resource constraint from the association between the supply attribute of the domain multiplex and the demand attribute of the associated consumer multiplex; Defining a binomial resource constraint between consumers in the consumer multiset in association with each problem expression; and (f) temporally backing the unary resource constraint and the binomial resource constraint. Applying a tracking algorithm to solve the problem. (17) In the step (e), a binomial resource constraint diagram is created from the relationship between the consumer group of the consumer multiset and an arbitrary order of evaluation of the consumer group. The method of (16) above, wherein the method is performed by specifying binary resource constraints between each other. (18) The method according to (16), wherein said temporal backtracking algorithm is of the class of performing a forward check with collision-oriented backjump. (19) A computer program product comprising a computer-readable medium having recorded thereon a computer program for calculating a solution of a constraint problem relating to resource allocation, wherein the resource allocation problem comprises: (i) resources for zero or more elements; A multiset representing each of the at least one domain including both availability and value; and (ii) at least one consumer and their resource requirements;
And computer code means represented by a multiplex set representing an arbitrary value constraint associated with each of the domain multiplex sets, and from each domain multiplex set, to each element of the domain, Computer code means for identifying a supply that is corresponding and orthogonal to the value, and from each consumer multiplex, for each consumer of the consumer multiplex, the demand that corresponds to the resource requirement and is orthogonal to any constraint on the required value. Computer code means for identifying and for each domain multiplex, computer code means for defining a unary resource constraint from an association between a supply attribute of the domain multiplex and a demand attribute of an associated consumer multiplex. , For each consumer multiset, the consumers in that consumer multiset Binomial resource constraints between Yuma each other,
Computer comprising computer code means for defining in association with individual problem expressions, and computer code means for applying the temporal backtrack algorithm to the unary and binary resource constraints to solve the problem・ Program products. (20) The computer code that defines the binomial resource constraint is based on a relationship between a consumer of the consumer multiset and an arbitrary order of evaluation of the consumer.
A term resource constraint diagram is created, and a binomial resource constraint between consumers is specified from the binomial resource constraint diagram. (19)
Computer program product as described in. (21) the computer code applying the algorithm applies a class of algorithms that performs a forward check with a collision-oriented back jump;
The computer program product according to (19). (22) A computer system programmed to calculate the solution of a resource allocation constraint problem, comprising: a memory for storing a computer program; and inputting the resource allocation problem as at least one domain of an element. Data input means for each of said elements having resource availability and at least one consumer each having resource requirements, wherein said resource allocation problem comprises: (i) zero or more. At least one containing both resource availability and value for the element
And (ii) a multiset representing at least one consumer and their resource requirements and any value constraints associated with each of the domain multisets, From the domain multiplex set, for each element in the domain, specify the supply that corresponds to the resource availability and orthogonal to the value, and from each consumer multiplex set, correspond to the resource requirements for each consumer of the consumer multiplex set Identify demands that are orthogonal to any constraints on required values, and for each domain multiplex, unary terms from the association between the supply attributes of the domain multiplex and the demand attributes of the associated consumer multiplex Define resource constraints and, for each consumer multiset, define the 2 Term resource constraints are defined in relation to individual problem expressions, and the resource assignment problem is responded to by applying a temporal backtracking algorithm to the unary and binomial resource constraints to solve the problem. And a processor for executing the computer program. (23) The processor creates a binomial resource constraint diagram from a relationship between a consumer group of the consumer multiset and an arbitrary order of evaluation of the consumer group.
The computer system according to (22), wherein a binomial resource constraint between consumers is specified from the term resource constraint diagram. (24) The computer system according to (22), wherein the processor applies a class of algorithm for performing a forward check with a collision-oriented back jump.

[Brief description of the drawings]

FIG. 1 schematically illustrates a problem with resource allocation.

FIG. 2 is a binomial constraint diagram for the problem of FIG. 1;

FIG. 3 is a diagram showing a generalized problem expression.

FIG. 4 shows a step-by-step solution of the problem of FIG. 1 according to the present invention.

FIG. 5 shows a graphical representation of resource availability and values for a further resource allocation problem.

6 shows a diagrammatic representation of the domain of the problem of FIG. 5 and a consumer multiset.

FIG. 7 is a constraint diagram of the problem of FIGS. 5 and 6;

FIG. 8 shows a solution to the problem of FIGS. 5 to 7 according to the present invention.

FIG. 9 illustrates a typical computer system that can implement the invention.

[Explanation of symbols]

100 computer system, 110 image display device, 120 Internet, 130 input device, 13
2 input device, 140 communication channel, 150 computer, 160 image interface, 162 storage device, 164 I / O interface, 166 control module, 170 memory, 172 I / O interface.

Claims (24)

[Claims] 1. A method for expressing a resource allocation problem, comprising: (a) defining the resource allocation problem by: (i) defining at least one domain including both resource availability and values for zero or more elements. (Ii) representing by a multiset representing at least one consumer and their resource requirements and any value constraints associated with each of said domain multisets; (b) Identifying, from each domain multiplex, a supply corresponding to resource availability and orthogonal to a value for each element of the domain; (c) from each consumer multiplex, each consumer of the consumer multiplex; Identifying the demands that correspond to the resource requirements and are orthogonal to any constraints on the required values. 2. The method of claim 1 wherein each domain multiplex is represented as a set of resource availability and value element pairs. 3. The method of claim 2, wherein each of said pairs comprises an arbitrarily complex set of values and resource availability. 4. The method of claim 1, wherein the consumer multiplex is represented as a set of resource requirements and value constraints. 5. The method of claim 4, wherein the value constraint comprises a variable or a value, or a combination of both. 6. For each domain multiplex, the supply is represented in terms of the sum of its base set and the number of occurrences of each element of the base set, and for the consumer multiplex the demand is The method of claim 1, wherein the method is expressed in terms of a sum of a set and the number of occurrences of each element of the basic set. 7. A method for expressing constraints associated with a resource allocation problem, comprising: (a) defining the resource allocation problem by: (i) at least including both resource availability and value for zero or more elements. (Ii) representing by a multiset representing at least one consumer and their resource requirements and any value constraints associated with each of said domain multisets; (B) identifying, from each domain multiplex, a supply corresponding to resource availability and orthogonal to a value for each element of the domain; and (c) from each consumer multiplex, the consumer Identifying, for each consumer of the multiset, a demand corresponding to the resource requirement and orthogonal to any constraint on the required value; (D) defining, for each domain multiplex, a unary resource constraint from an association between a supply attribute of the domain multiplex and a demand attribute of an associated consumer multiplex; and (e) each consumer multiplex. Defining a set of binomial resource constraints between consumers in the consumer multiset in relation to the individual problem expressions. 8. A unary resource constraint is defined for each consumer, and the supply of each consumer determines the consumer's view of the domain with that of the domain having a supply greater than the demand of the consumer. The method of claim 7, wherein the method is limited to elements only. 9. The method of claim 7, wherein for any given order of assignment of values to consumers, a binary resource constraint exists between one consumer and all subsequently assigned consumers. . 10. Assigning a value to a consumer realizes a binomial resource constraint that is dependent on the satisfied unary resource constraint of the consumer, so that the allocation by the amount of demand of the consumer is achieved. 10. The method of claim 9, wherein the supply of the reduced value is reduced, and availability restrictions constrain the assignment of this same value to the next consumer. 11. The method of claim 7, wherein each domain multiplex is represented as a set of resource availability and value element pairs. 12. The method of claim 11, wherein each of said pairs comprises an arbitrarily complex set of values and resource availability. 13. The method of claim 7, wherein the consumer multiplex is represented as a set of resource requirements and value constraints. 14. The method of claim 13, wherein said value constraint comprises a variable or a value, or a combination of both. 15. For each domain multiplex, the supply is represented in terms of the sum of its base set and the number of occurrences of each element of the base set. The method of claim 7, wherein the method is expressed in terms of a sum of a set and the number of occurrences of each element of the basic set. 16. A method for solving a constraint problem relating to resource allocation using a computer, comprising: (a) solving the resource allocation problem; and (i) determining both resource availability and values for zero or more elements. And (ii) represented by a multiset representing at least one consumer and their resource requirements, and any value constraints associated with each of said domain multisets. (B) identifying, from each domain multiplex, a supply corresponding to resource availability and orthogonal to a value for each element of the domain; (c) from each consumer multiplex, For each consumer in the consumer multiset, identify demands that correspond to resource requirements and are orthogonal to any constraints on required values (D) defining, for each domain multiplex, a unary resource constraint from an association between a supply attribute of the domain multiplex and a demand attribute of an associated consumer multiplex; (e) For each consumer multiset, defining binomial resource constraints between the consumers in the consumer multiset in association with the individual problem expressions; and (f) defining the unary resource constraint and the binomial resource constraint in time. Applying a backtracking algorithm to solve the problem. 17. A step (e) comprising: creating a binomial resource constraint diagram from a relationship between a consumer group of the consumer multiset and an arbitrary order of evaluation of the consumer group; 17. The method of claim 16, wherein the method is performed by identifying binary resource constraints between consumers from. 18. The method according to claim 17, wherein said temporal backtracking algorithm comprises a forward link with collision oriented back jump.
17. The method according to claim 16, which is of the class that performs a check. 19. A computer program product comprising a computer readable medium having recorded thereon a computer program for calculating a solution to a resource allocation constraint problem, the resource allocation problem comprising: (i) zero or more elements; A multi-set representing each of at least one domain including both resource availability and value for: (ii) at least one consumer and their resource requirements, and associated with each of said domain multi-sets Computer code means expressed by a multiset representing an arbitrary value constraint; and from each domain multiset, for each element of the domain,
Computer code means for identifying the supply corresponding to the resource availability and orthogonal to the value; and from each consumer multiplex, any constraints on the resource requirements and required values for each consumer of the consumer multiplex. For each domain multiplex set and computer code means for identifying a demand orthogonal to, a unary resource constraint is defined from the association between the supply attribute of the domain multiplex set and the demand attribute of the associated consumer multiset. Computer code means, for each consumer multiset, computer code means for defining binomial resource constraints between consumers in the consumer multiset in association with individual problem expressions, and said unary resource constraints and Apply temporal backtracking algorithms to resource constraints To, computer program product comprising a computer code means for solving the problem. 20. The computer code defining the binomial resource constraint creates a binomial resource constraint diagram from the relationship between the consumers of the consumer multiset and an arbitrary order of evaluation of the consumer. 20. The computer according to claim 19, wherein a binary resource constraint between consumers is specified from the term resource constraint diagram.
Program products. 21. The computer program product of claim 19, wherein the computer code applying the algorithm applies a class of algorithms that performs a forward check with a collision-directed back jump. 22. A computer system programmed to calculate the solution of a constraint problem relating to resource allocation, comprising: a memory for storing a computer program; and inputting the resource allocation problem as at least one domain of an element. Data input means used to
Each of the elements has a resource availability and at least one
A data entry means wherein each of the consumers has resource requirements; and a multiset representing each of the at least one domain including both (i) resource availability and values for zero or more elements. And (ii) a multiset representing at least one consumer and their resource requirements, and any value constraints associated with each of the domain multisets, and from each domain multiset, For each element of, specify a supply that corresponds to resource availability and is orthogonal to the value, and from each consumer multiplex set, for each consumer of that consumer multiplex set, any constraints on resource requirements and required values Identify the demands that are orthogonal to, and for each domain multiplex, provide the supply attributes of the Unary resource constraints are defined from the association between the demand attributes of the consumer multisets, and for each consumer multiset, binomial resource constraints between consumers in the consumer multiset are defined in association with individual problem expressions. A processor that executes the computer program in response to the resource allocation problem so as to solve the problem by applying a temporal backtrack algorithm to the unary and binary resource constraints. Computer system. 23. The processor creates a binomial resource constraint diagram from a relationship between a consumer group of the consumer multiset and an arbitrary order of evaluation of the consumer group. 23. The computer system of claim 22, specifying binary resource constraints between. 24. The computer system of claim 22, wherein said processor applies a class of algorithms to perform forward checks with collision-oriented back jumps.